In part 3 of the story, the policeman who arrested Tajomaru tells us that Tajomaru is "a notorious brigand." A "brigand" is a robber who ambushes people in remote areas. Tajomaru, the policeman says, is also suspected of murdering another woman. This criminal background suggests that Tajomaru might have been capable of committing murder. The policeman also tells us that Tajomaru had in his possession, when he was arrested, a bow and arrows that looked very much "like the ones owned by the dead man." Indeed, this seems to be enough evidence for the policeman, who proclaims, "Then Tajomaru must be the murderer."
In part 7 of the story, Tajomaru seems to confess to the murder. A confession is usually of course a very good reason to believe that the confessor is guilty. Tajomaru's confession begins, "I killed him." Tajomaru says that he killed the man because he wanted the man's wife for himself. He also says, "To me killing isn't a matter of such great consequence as you might think." Tajomaru says that he intended at first not to kill the woman's husband, but only to tie him up. However, Tajomaru raped the woman, and afterwards, feeling ashamed, she told Tajomaru that either he or her husband had to die, because, she said, "it was more trying than death to have her shame known to two men."
It was at this point, Tajomaru says, that he was "seized" by "a furious desire to kill" the husband. Tajomaru's professed "desire" to kill the husband, coupled with his seemingly unambiguous proclamation, "I killed him," is perhaps the most convincing evidence that he is indeed guilty of the murder.
At the end of Tajomaru's confession, however, he suggests that he did not in fact kill the man. Determined to kill the woman's husband, but wanting to do so with honor, Tajomaru says that he untied the husband and challenged him to a duel. When they started fighting, he says, the woman ran away. Tajomaru then ran after the woman, leaving the husband still alive. If we believe this account to be true, then we can assume that when Tajomaru earlier said, "I killed him," he was speaking figuratively, not literally. He perhaps meant that he as good as killed the husband by raping his wife and by forcing his wife to flee. After this, the husband was likely not alive in the way that he was before.